A three-phase network is, indeed, either grounded or ungrounded. What that means, to my understanding, is that, simply speaking, the neutral point on a wye connection can be either grounded or not. What I really mean when I say "ungrounded" is the situation when there's no closed zero-sequence path for current to flow. A delta-wye grounded transformer is commonly referred to as a grounding bank, because the delta side of the transformer can be left un-terminated--still connected in delta but not connected to anything else--and there can still be zero-sequence current flow on the wye-grounded side. Buried delta tertiaries in transformers, which are deliberately designed not to be terminated to anything, act in this manner; these buried delta tertiary windings also help stabilize the phase voltage during regular system operation. Zero-sequence current circulates in the delta winding. Also, a transformer with windings connected in zig-zag provides a "ground reference" to the delta side of a transformer; thus making a zero-sequence path for current on the delta side of the transformer.
In three-phase power systems, if the system is not grounded, for all intents and purposes, there will be no current flow to ground in a phase-to-ground fault. In actuality, there will be current flow to ground in an ungrounded system with a phase-to-ground fault due to the natural capacitive coupling to ground of the system. Therefore, the fault current, or ground current, will be returned by the distributed capacitance in the two unfaulted phases. However the system, assuming it's 3-phase, will have a transient neutral voltage shift with the one phase that's grounded phase-to-ground voltage equal to zero volts and the other two phase to ground voltages raised in magnitude by the square root of three (the line voltage). This is what's really characteristic and important about an ungrounded three-phase system, not necessarily the current. Therefore, an ungrounded system needs line-to-line voltage insulation to compensate for a ground fault. Usually, ungrounded three-phase systems are not recommended or seen very often, but they are used where continuity of electrical service is of the highest priority to minimize production process interruptions in some industrial plants. Finally, the three-phase voltage triangle will remain intact with 120 degree separation between the voltages; however, the neutral to ground voltage is shifted, as mentioned above, to equal the zero sequence voltage.
Now, looking at a three-phase grounded system, the return path for a phase-to-ground or phase-to-phase to ground fault is the ground and the neutral connected to ground on the wye side of a wye-delta transformer or on either side of a grounded wye-grounded wye transformer. Therefore, the phase to ground current is most likely greater in magnitude when a wye-delta transformer, also known as a grounding bank, is nearby than the three-phase fault current. A three-phase fault, even if it's touching ground, will never produce ground (zero-sequence) current. I believe all that does is set the voltage at the location touching ground equal to the reference potential (usually taken as zero), again referring to a three-phase fault that's also touching ground.
When I mention a return current through distributed capacitance, I am referring to the fact that there will be a return current in both the unfaulted phases on an ungrounded system with a phase-to-ground fault. The distributed capacitance makes this possible. I implied that this fault and return current is negligible, in the first sentence of my previous comment: "... if the system is not grounded, for all intents and purposes, there will be no current flow to ground in a phase-to-ground fault." The important thing to consider is the voltage; this is not negligible. Finally, in a perfectly balanced three-phase system, the return path for current flowing in one phase is the other two phases. One can even ground the neutral point of this system and no current will flow to ground, even if there's a zero-sequence path for it to flow. However, a perfectly balanced system is impractical for utilities or industrial power systems; so, there will be a zero-sequence current flow, due to the imbalance, where there's a circuit for it to flow.