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Boost converters and battery chargers

Other Parts Discussed in Thread: BQ24195

After reading about the TPS61021 boost converter (running 3.3V from a battery) I wondered:

What about the battery charging circuit?  Is there a single IC that does both?

When charging from a standard USB connector, a single integrated design would charge the battery AND drive the load. When the battery reaches fully charged, the device would keep it at 100% while continuing to drive the load.

When the USB charger is removed, this integrated solution would  then act as an UPS - and switch over to the battery.

Does such a device exist?