A disintegrable tubular anchoring system comprises a frustoconical member; a sleeve with at least one first surface being radially alterable in response to longitudinal movement of the frustoconical member relative to the sleeve, the first surface being engagable with a wall of a structure; a seal with at least one second surface being radially alterable; and a seat having a land being sealingly engagable with a removable plug runnable thereagainst. The frustoconical member, sleeve, seal, and seat are disintegrable and independently comprise a metal composite which includes a cellular nanomatrix comprising a metallic nanomatrix material; and a metal matrix disposed in the cellular nanomatrix. A process of isolating a structure comprises disposing the disintegrable tubular anchoring system in the structure; radially altering the sleeve to engage a surface of the structure; and radially altering the seal to the isolate the structure.