I know 私は田中さんにプレゼントをもらいました means "I received a gift from Mr/Mrs Tanaka" and 私は田中さんにプレゼントをあげました means "I gave a gift to Mr/Mrs Tanaka".
What I'm wondering is, can もらいます・あげます sentences work without the ni particle?
In that case would 田中さんはプレゼントをもらいました mean "Mr/Mrs Tanaka received a gift" and 田中さんはプレゼントをあげました - Mr/Mrs Tanaka gave a gift? Or is it all wrong? And does the person who receives/gives this to/from Mr/Mrs Tanaka is always implied to be us, or can it be anybody?