If you have a Transmission bittorrent server running somewhere and allow remote access to it (SSL supported), then you can use Transdroid on your phone to locate torrents and start them off on your server remotely. It has a search function, includes a list of popular torrent servers you can search from within the app, and if you touch one of the links it finds it will upload it to the remote PC and start the torrent running. Couldn't be easier. Just as easy to monitor uploads and downloads and ratios and stop or pause any torrents you think have done their dash in terms of uploading data.
Below is a screen capture of a torrent I've just started from my phone. I have a version of the server for the LAN and another version of the server for access from anywhere on the Internet.